Aircraft: LARGE TRANSPORT
Phase of flight: Climb
Anomaly: ATC Issue All Types; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance

Aircraft dispatched [from] CLT filed at FL380. Aircraft was step climbed from CLT in 1;000 foot increments since leaving CLT. About halfway through the flight; we were still at approximately 14;000 feet just north of Savannah; Georgia. ATC issued us a heading off course for a climb. I believe they cleared us to FL230 and asked us to expedite our climb. We were already cruising at an ATC assigned speed at the time of 280 knots. I set FL230 in the altitude alert window and pulled 'OPEN CLIMB.' I spun the airspeed down to 250 knots to expedite the climb. At approximately 15;400 feet; ATC asked us to level off at 16;000 feet. I reset the altitude alert window to 16;000 feet; unfortunately the aircraft was now climbing in excess of 3;000 feet per minute. The autopilot captured the altitude (ALT*) at approximately 15;800 feet. The autopilot was unable to level the aircraft at 16;000 feet and the aircraft overshot the altitude. I intervened and attempted to vertical speed the aircraft back to the 16;000 feet altitude. We hit a max altitude overshoot of approximately 16;500 feet. I did not disconnect the autopilot and manually force a level off because the aircraft was halfway through the flight and flight attendants were in the aisles with carts serving the passengers. If I had intervened and manually pushed the aircraft over to maintain the 16;000 feet altitude; it would have imposed serious negative 'G' force on the aircraft and caused serious injury to the crew and passengers. We received no TA alert or RA during the event. It was a late and unexpected level off call from ATC after requesting an expedited climb. The incident appears to be a controller operational error. The Controller may have been frustrated by his inability to get us to our cruise altitude because of the amount of traffic during our flight. I am at a loss as to why he directed us off course for a climb on a heading that apparently put us in conflict with other traffic. After the incident was over; we did notice traffic at 17;000 feet; but was not close enough to cause a 'TA' or 'RA' on TCAS. The new generation of aircraft are designed to be flown on automation and react according to their design specifications which may differ from the expectations of air traffic controllers. I have noticed this many times during descents when asked to expedite descents. Most aircraft are now descending at their optimum descent point which is idle power. There is little or no capability for pilots to expedite when asked to go down and slowdown at the same time. I don't have the answer to this problem other than to say that human error is a fact of life and if we continue trying to jam more work (aircraft or spacing) into an already overcrowded environment which provides little or no room for human error; we will continue to see operational errors increase. Pilot reports of going above newly assigned altitude because the Controller was late in assigning the new altitude. For safety reasons the pilot didn't want to give the passengers or attendants a G force ride attempting to manually over-ride the aircraft.